用数学归纳法证明0.1+0.01+0.001+.+0.1的n次方=((1-0.1的n次方)/9)
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![用数学归纳法证明0.1+0.01+0.001+.+0.1的n次方=((1-0.1的n次方)/9)](/uploads/image/z/13911616-64-6.jpg?t=%E7%94%A8%E6%95%B0%E5%AD%A6%E5%BD%92%E7%BA%B3%E6%B3%95%E8%AF%81%E6%98%8E0.1%2B0.01%2B0.001%2B.%2B0.1%E7%9A%84n%E6%AC%A1%E6%96%B9%3D%EF%BC%88%EF%BC%881-0.1%E7%9A%84n%E6%AC%A1%E6%96%B9%EF%BC%89%2F9%EF%BC%89)
用数学归纳法证明0.1+0.01+0.001+.+0.1的n次方=((1-0.1的n次方)/9)
用数学归纳法证明0.1+0.01+0.001+.+0.1的n次方=((1-0.1的n次方)/9)
用数学归纳法证明0.1+0.01+0.001+.+0.1的n次方=((1-0.1的n次方)/9)
当n=1时候,左边=0.1,右边=(1-0.1^1)/9=0.1 左边=右边,等式成立 假设n=k-1时候,等式成立 那么n=k时候,0.1+0.01+0.001+.+0.1的k次方 ==((1-0.1的k-1次方)/9)+0.1的k次方 ==(1-0.1的k-1次方)+9*0.1的k次方)/9 =(1-0.1的k-1次方+0.9*0.1的k-1次方)/9 =(1-0.1*0.1的k-1次方)/9 =1-0.1的k次方)/9